Proposition 4.1 ([1]}, [2]}, [3]})  
Suppose that \(p^{-1}+q^{-1}=r^{-1}\) . If \(S\in {L}_{p,\infty }\)  and \(T\in {L}_{q,\infty }\) , then \(ST\in {L}_{r,\infty }\)  with norm inequality,
\(\Vert ST\Vert _{{L}_{r,\infty }} \le \gamma (p,q)\Vert S\Vert _{{L}_{p,\infty }} \Vert T\Vert _{{L}_{q,\infty }}, \qquad \gamma (p,q):=p^{-\frac{1}{q}}q^{-\frac{1}{p}} (p+q)^{\frac{1}{p}+\frac{1}{q}}.\) 
